The club's record signing has lost his place in the side to Ousmane Dembele but started against Rayo with the Frenchman rested ahead of Wednesday's game against Lyon.
But Coutinho, who cost an initial €140 million when he joined from Liverpool last January, was unable to make the impact which would have given coach Ernesto Valverde a headache going into the Champions League game.
Barcelona player ratings: Messi, Suarez shine in comeback victory
"Philippe is having a good season," Pique told reporters when asked about the fan reaction to Coutinho's 80th-minute substitution.
"Obviously, he cost a lot and that means there are higher expectations surrounding his performances. It is what it is. You have to accept the reaction of the fans because at the end of the day they're our supporters, you have to respect [their opinion].
"We -- his teammates and people at the club -- have to give him all the support in the world. We need him at his best in the final stage of the season and I'm sure he will be."
Valverde also attempted to play down the negative reaction Coutinho was subjected to from parts of the stadium.
"We're at a club where there's an incredible demand to win," the Barca coach said in a news conference. "That's the case at all clubs, but especially here.
"We don't have to give [the whistles aimed at Coutinho] too much importance. He was fighting all game to score. We're always hoping our players are going to pull a rabbit out of the hat, but it's not always the case.
"Sometimes things come off, sometimes they don't. But his work rate is there to be seen for everyone. The secret is in persevering."
After a run of four away games against Lyon, Sevilla and Real Madrid (twice), Pique was happy to overcome Rayo in what he felt was a potential banana skin before the midweek visit from Lyon.
"We've had a tough run of games," the defender added. "[Rayo] was, in theory, a more winnable match, but games like this are historically difficult to play. Before Roma [last season], we didn't play well against Leganes.
"We have to try and focus on Wednesday. We have three objectives in our head [La Liga, the Copa del Rey and the Champions League] but there's a long way to go. Lyon is a final. All or nothing. We're now focused on that."